Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 9 x + 92 x^{2} + 428 x^{3} + 2116 x^{4} + 4761 x^{5} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.529414612431$, $\pm0.610177845141$, $\pm0.669162156677$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.26626183576.1 |
| Galois group: | $S_4\times C_2$ |
| Cyclic group of points: | yes |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $19574$ | $179650172$ | $1732669672838$ | $21865784379858016$ | $267034646410161653024$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $33$ | $633$ | $11697$ | $279217$ | $6445978$ | $148020477$ | $3404742087$ | $78311341905$ | $1801152038571$ | $41426514039688$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains no Jacobian of a hyperelliptic curve, but it is unknown whether it contains a Jacobian of a non-hyperelliptic curve.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The endomorphism algebra of this simple isogeny class is 6.0.26626183576.1. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 3.23.aj_do_aqm | $2$ | (not in LMFDB) |